Magnetic moment
Next we need to introduce the concept of magnetic moment, which is the moment of the couple exerted on either a bar magnet or a current loop when it is in an applied field. Again we can define the magnetic moment either in terms of poles or in terms of currents.Imagine a bar magnet is at an angle θ to a magnetic field,H, as shown in Fig. 1.5. We showed in Section
that the force on each pole, F = pH. So the torque acting on the magnet, which is just the force times the perpendicular distance from the center of mass, is where m = pl, the product of the pole strength and the length of the magnet, is the magnetic moment. (Our notation here is to represent vector quantities by bold italic type, and their magnitudes by regular italic type.) This gives a definition:The magnetic moment is the moment of the couple exerted on a magnet when it is perpendicular to a uniform field of 1 oersted. Alternatively, if a current loop has area A and carries a current I , then its magnetic moment is defined as m = IA.
Magnetic dipole
A magnetic dipole is defined as either the magnetic moment, m, of a bar magnet in the limit of small length but finite moment, or the magnetic moment, m, of a current loop in the limit of small area but finite moment. The field lines around a magnetic dipole are shown in Fig. 1.6. The energy of a magnetic dipole is defined
as zero when the dipole is perpendicular to a magnetic field. So the work done(in ergs) in turning through an angle dθ against the field is dE = 2(pH sin θ) and the energy of a dipole at an angle θ to a magnetic field is.This expression for the energy of a magnetic dipole in a magnetic field is in cgs units. In SI units the energy is E = −μ0m · H. We will be using the concept of magnetic dipole, and this expression for its energy in a magnetic field, extensively throughout this book.
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